Flexi joint. It allows the engine to move on the engine mounts as it should and the exhaust to be fixed toe the car and not rattle.

You need to take it to an exhaust place. They may be able to just replace the joint but you may need a new system. Only then can you get a quote.

Looks like the catalytic converter. Take it to a muffler shop. Prob cost around 200-300 depending on your make/model

Flex pipe

It is the flexy joint that needs replacing.

I saw this why changing my car oil.